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I was reading this information related to aerosol, especially aerosol optical depth of the MISR and MODIS instruments. I didn't actually get what bias means in the context of the AOT retrievals of these instruments.

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These instruments sense reflectance from the earth's surface in several spectral bands. A theoretically motivated, but somewhat ad hoc, formula is used to estimate aerosol properties from carefully pre-processed sensor data. Because the relationships among the aerosol properties and what is measured by the instrument are nonlinear, complex, and potentially affected by extraneous factors (for example, a separate formula altogether is used for land versus water), it is essential to "field truth" the results through comparison to independent objective aerosol measurements.

This is a form of calibration. In calibrating any instrument we recognize that the instrument's readings may--for certain ranges of readings or combinations of underlying conditions--have a different value, on average, than the true value. Bias is the numerical difference between the average instrument reading and the true value. A "high" or positive bias occurs when the instrument reading is greater than the true value on average; otherwise, the bias is either zero or negative.

Bias typically varies from one value to another. For example, p. 65 of the MODIS algorithm documentation (2009) compares MODIS to AERONET sunphotometer values to "validate" the MODIS results. The bias is depicted by the vertical discrepancies between the plotted points and an imaginary diagonal line with equation $y=x$.

The bias will be estimated by collecting pairs of (field truth, instrument) readings. It is rare to see any distinction made between the true bias (how the instrument actually behaves on average) and estimates of the bias; the word "bias" loosely applies to both concepts. The two values will be close when the estimates are made from many independent pairs of readings.

Finally, the results of such measurements should be expressed using methods of "inverse regression," or a generalization thereof, as explained in a summary by Lavagnini & Magno writing in Mass Spectrometry Reviews (2007). This procedure aims to put "error bands" around the true value, given the instrument reading. After all, in practice, you will be relying on the instrument reading--you won't have anything better at most locations--so you will want some measure of how reliable those readings might be. Don't expect to see very many applications of this procedure, though: it seems not to be well enough known in many fields.

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